Optimal Online Discrepancy in Linear Time
Given online vectors $v_t \in \mathbb{R}^d$ with $\|v_t\|_2 \le 1$, can signs $\varepsilon_t \in \{-1, 1\}$ be chosen in $O(dT)$ total time so that every prefix has $\ell_\infty$ discrepancy $O(\sqrt{\log T})$ with high probability? The previous optimal algorithm ran in time exponential in $T$ and $d$.
Exact FrontierDelta
Scope and record
Occurred: Jul 6, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.
Canonical aliases: Optimal Online Discrepancy in Linear Time · Linear-time discrepancy
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Ishaq Aden-Ali
human · human collaborator
GPT-5.5 Pro Extended
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Ishaq Aden-Ali
This event attributed to GPT-5.5 Pro Extended